Ugandan Defence Minister Crispus Kiyonga said that he was mediating discussions to help both sides reach a settlement that would end a violent rebellion that has sucked in Uganda and Rwanda, which both face charges of backing the rebels.
The M23 group said that its president Bishop Jean-Marie Runiga was leading the rebels in the talks.
A regional summit of the International Conference of the Great Lakes Region in Kampala, including DRC President Joseph Kabila and Ugandan President Yoweri Museveni, on Saturday called on the rebels to leave Goma and urged Kabila to listen to the "legitimate grievances" of M23.
Despite the regional leaders' demands for the rebel forces to withdraw from Goma, M23 soldiers were visibly in control of the city on Sunday.
The group also still held Sake, a contested town 25km west of Goma.
The DRC army attacked the town on Saturday, but M23 retained control.
Runiga said that withdrawal from Goma was "under consideration" and, while M23 did not oppose the idea "in principle," no decision had been taken yet, according to M23 spokesperson Vianney Kazarama.
Runiga is still in Kampala and no official response to the demands from the regional summit is expected before his return to the DRC, said Kazarama in Goma.
"We are waiting to hear from Runiga when he will be back from Kampala," said Kazarama.
Kabila also met Runiga in Kampala briefly, said M23's deputy spokesperson Amani Kabasha.
"Since May we have asked to meet President Kabila," said Kabasha.
"At least now there has been contact and the door is open for talks to find the durable peace that eastern Congo needs."
Government troops remain in Minova, 25km south of Sake, following a failed attack on M23 on 22 November.
Unruly DRC army soldiers had looted residents for the third night running, according to a United Nations official in the town.
UN peacekeepers patrolled Minova throughout the night to protect civilians from the rampaging government troops.